There is a bit of trial and error here for the most experienced of us. The North Atlantic DAMEE runs were done with upstream bias advection of velocity and tracer, without explicit horizontal smoothing. If you look for it, you can see residual 2 dx noise, especially in mid-depth vertical velocities. Another variable is how smooth is "smooth enough".

Something in the model is producing numerical 2 dx noise at some unknown rate. The Laplacian smoothing will damp that out on a timescale of

t_damp = (2 dx)^2 / ((2 pi)^2 nu)

or

t_damp = (dx)^2 / (pi^2 nu)

You can work out how long it will take to smooth things at 2 dx from this, also things at larger scales, such as that 8 dx eddy you really want to keep. The corresponding biharmonic formula is:

t_damp = (dx)^4 / (pi^4 nu)

Other decisions are whether to rotate the mixing or not. There is some question about the correctness of the u,v rotation and it is advised not to rotate the viscosity. For diffusion, we like to rotate to z surfaces at least.

Kate HedstrÃ¶m

kate@arsc.edu